Test Index

Ratio and Proportion

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Question : 2 of 112

Marks: +1, -0

If

(3a + 2b) : (3a – 2b) = 9 : 5

a : b

is

$7 : 2$
$3 : 2$
$7 : 3$
$2 : 3$

Solution:

Concept:

Use cross-multiplication to convert the given ratio into a linear equation, then solve for the ratio

a:b

.

Explanation:

Given:

\frac{3a+2b}{3a-2b} = \frac{9}{5}

.

Cross-multiply:

5(3a+2b) = 9(3a-2b)

.

Expand:

15a + 10b = 27a - 18b

.

Bring terms with

a

to one side and

b

to the other:

10b + 18b = 27a - 15a

.

Simplify:

28b = 12a

.

Divide both sides by

4

:

7b = 3a

.

Thus,

\frac{a}{b} = \frac{7}{3}

, i.e.,

a:b = 7:3

.

Answer:

Option C:

7:3

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